Algebra Examples

$28 - \frac{x}{2} = \frac{x}{5}$

Step 1

Subtract $\frac{x}{5}$ from both sides of the equation.

$28 - \frac{x}{2} - \frac{x}{5} = 0$

Step 2

Simplify $28 - \frac{x}{2} - \frac{x}{5}$ .

Tap for more steps...

Step 2.1

To write $- \frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$28 - \frac{x}{2} \cdot \frac{5}{5} - \frac{x}{5} = 0$

Step 2.2

To write $- \frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$28 - \frac{x}{2} \cdot \frac{5}{5} - \frac{x}{5} \cdot \frac{2}{2} = 0$

Step 2.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.3.1

Multiply $\frac{x}{2}$ by $\frac{5}{5}$ .

$28 - \frac{x \cdot 5}{2 \cdot 5} - \frac{x}{5} \cdot \frac{2}{2} = 0$

Step 2.3.2

Multiply $2$ by $5$ .

$28 - \frac{x \cdot 5}{10} - \frac{x}{5} \cdot \frac{2}{2} = 0$

Step 2.3.3

Multiply $\frac{x}{5}$ by $\frac{2}{2}$ .

$28 - \frac{x \cdot 5}{10} - \frac{x \cdot 2}{5 \cdot 2} = 0$

Step 2.3.4

Multiply $5$ by $2$ .

$28 - \frac{x \cdot 5}{10} - \frac{x \cdot 2}{10} = 0$

Step 2.4

Combine the numerators over the common denominator.

$28 + \frac{- x \cdot 5 - x \cdot 2}{10} = 0$

Step 2.5

Simplify each term.

Tap for more steps...

Step 2.5.1

Simplify the numerator.

Tap for more steps...

Step 2.5.1.1

Factor $x$ out of $- x \cdot 5 - x \cdot 2$ .

Tap for more steps...

Step 2.5.1.1.1

Factor $x$ out of $- x \cdot 5$ .

$28 + \frac{x (- 1 \cdot 5) - x \cdot 2}{10} = 0$

Step 2.5.1.1.2

Factor $x$ out of $- x \cdot 2$ .

$28 + \frac{x (- 1 \cdot 5) + x (- 1 \cdot 2)}{10} = 0$

Step 2.5.1.1.3

Factor $x$ out of $x (- 1 \cdot 5) + x (- 1 \cdot 2)$ .

$28 + \frac{x (- 1 \cdot 5 - 1 \cdot 2)}{10} = 0$

Step 2.5.1.2

Multiply $- 1$ by $5$ .

$28 + \frac{x (- 5 - 1 \cdot 2)}{10} = 0$

Step 2.5.1.3

Multiply $- 1$ by $2$ .

$28 + \frac{x (- 5 - 2)}{10} = 0$

Step 2.5.1.4

Subtract $2$ from $- 5$ .

$28 + \frac{x \cdot - 7}{10} = 0$

Step 2.5.2

Move $- 7$ to the left of $x$ .

$28 + \frac{- 7 \cdot x}{10} = 0$

Step 2.5.3

Move the negative in front of the fraction.

$28 - \frac{7 x}{10} = 0$